Convergence of the multigrid $V$-cycle algorithm for second-order boundary value problems without full elliptic regularity

The multigrid V -cycle algorithm using the Richardson relaxation scheme as the smoother is studied in this paper. For second-order elliptic boundary value problems, the contraction number of the V -cycle algorithm is shown to improve uniformly with the increase of the number of smoothing steps, without assuming full elliptic regularity. As a consequence, the V -cycle convergence result of Braess and Hackbusch is generalized to problems without full elliptic regularity.

• Type: Journal
• Year: 2002
• Where: MOC
• Authors: Susanne C. Brenner
• Keywords: Contraction Number, Elliptic Boundary Value, MOC 2002, Richardson Relaxation Scheme